Q190 / 270 · NDA 2019 (Phase 2) · Mathematics

A binary number is represented by $(c d c c d d c c c d d d)_2$, where $c \gt d$. What is its decimal equivalent?

  • A
    1848
  • B
    2048
  • C
    2842
  • Correct answer
    D
    2872

Solution

$\begin{aligned} & (c d c c d d c c c d d d)_2 \\ & \because c \gt d \\ & \therefore c=1 \text { and } d=0 \\ & \therefore \text { no }=(101100111000)_2 \\ & \therefore \text { decimal equivalent }= \\ & 2^{11}+2^9+2^8+2^5+2^4+2^3 \\ & =2048+512+256+32+16+8 \\ & =2872\end{aligned}$

Hence, the correct answer is option: 'D'.

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